I'd go with a tone on tone... texture over color instead of introducing another pattern.

I don't like either but I do like the pillow on the chair . So maybe texture over print . How about mongolian lamb pillows in a color from the chair for instance .

Good idea so the textures should be all blue?

All these pillow covers are from Etsy stores.

From what you’ve shown, the color scheme is pretty bland and similar colors. I like the print chair, so I’d consider some solid color pillows in the deepest colors from the chair, for more contrast and more life. I like pattern mixing, but it’s just harder when shopping ready- made items. A stripe or check item works- here I’d also look for more- dark- than- light colors if using an additional print.
BTW I only use pillows with zipper covers that are washable ( many that day dry clean can be hand-washed or on delicate and lay flat to dry). They’re harder to find and can’t just walk into a discount store & find them at will- I keep my eye out for “ my” colors and patters and fabrics when in stores because randomly they’ll have something I can use. and also search online and have found them in unexpected sites, like Home Depot, Target, in addition to the pricier Pottery Barn.
I understand texture and like adding it , but many of the furry pillows are either not washable or to me don’t have a good feel to touch.

I wouldn't add a pattern pillow, as it would be too busy next to the chair. I would, however suggest a solid color pillow in the gray that is either textured or smooth, to add interest but still compliment the chair color.

In "neutral" settings, it is best to use a lot of "textures" along with a few darker tones for contrast. Velvets are great (cotton), tweeds, fluffy fabrics, etc. A charcoal velvet might be nice, but I like some color so I would do a velvet lumbar for the chair.